A fictitious domain method for Dirichlet problems using mixed finite elements

In this note, we propose an approximation of the solution of a Dirichlet pr oblem by means of a fictitious domain method. The original problem is repla ced by a saddle-point problem defined on the fictitious domain Omega. To di scretize the continuous problem, we use Raviart Thomas mixed finite element s. We give an error estimate and we prove that the condition number of the linear system to solve is independent of the discretization parameter. (C) 1999 Elsevier Science Ltd. All rights reserved.